Is there a way to insert Log base-something into Google Calculator?

For base $b=10$ we can use log_10(n) or log(n)

For base $b=e$ we can use ln(n)

For base $b=2$ we can use log_2(n) or lg(n)

Other bases aren't implemented, so we use the Change of Base Rule, namely $\log_b(n) = \frac{\ln(n)}{\ln(b)}$ which we put into the calculator as ln(n)/ln(b). This works with any other base, so log(n)/log(b) would be the same.